When Base Stations Meet Mobile Terminals, and Some Results Beyond

Wireless networks are designed based on population patterns. To densify networks, the organization of a cellular network is, therefore, done according to user density to minimize the cost of investment. Since populations do not appear in the form of a regular geometric grid, the planning of networks should not either. Instead, a two-dimensional Poisson process is believed to be a good match of reality. This has been the basis for groundbreaking work by various researchers showing how stochastic geometry based on independent Poisson point processes can be applied. However, to minimize cost and maximize capacity, cellular networks are densified wherever the user density is high. Hence, modelling users and base stations as independent Poisson processes does not match reality, but instead, generates "worst case" scenarios and therefore, weak lower bounds. Instead, the user and base station processes must reflect this correlation to be able to model reality suitably. In this talk, we shall describe our efforts towards realizing this goal. During our investigations, we find that using a Neyman-Scott process to model users clustered around base stations could be a viable alternative. When densifying cellular networks even further, a hierarchy of cells is used, i.e. micro base stations are placed where capacity hot spots appear. Once again, correlating one process with the other (i.e. introducing a correlation among the base station processes) is pivotal for capturing reality accurately. To this end, we shall talk about our work on models using stationary Poisson cluster processes and how they can be used to study such networks. Lastly, if time permits, we then will also talk about linear algebra and matrix theory; hopefully extending the view of what is known today.